You have a few issues here:
- This system can only support a SATA II (3.0 Gb/s), most drives today are SATA III (6.0 Gb/s) and won’t work via the internal SATA port.
- Cloning software is very iffy! They work on a block by block basis so any corruption on your older drive get carried over, in some cases the remap is not complete so the new drive won’t work properly. Garbage In, Garbage Out! You also carry over all of the junk your system has built-up. I gave up using it over 10 years ago as it was such a pain and very wasteful. I use Apple’s TimeMachine and Migration Assistant only now. FYI: None of the cloning apps support APFS file system.
- You could have also damaged the SATA cable
So you’ll need to review your SSD’s spec sheet to see if it lists SATA II support. If its not listed then you’ll need to get another drive.
As an example, here is the Samsung 860 EVO SSD spec sheet Note the Interface line lists 3.0 Gb/s (SATA II) so this drive is able to support multiple I/O speeds (auto sense). While if we look at this drive Western Digital Blue SSD spec sheet Note the Interface only lists 6.0 Gb/s (SATA III) this SSD won’t work in your system (fixed speed). There are still some SATA II (3.0 Gb/) only drives like OWC Mercury Electra 3G
You’ll need to get a fresh copy of your OS as the certificates in the older installers will mess you up! If you've got an old macOS install image, it will probably stop working today. Here’s how to get the needed newer OS installer: How to get old versions of macOS Using your still working HDD which you are replacing reformat the SSD to GUID and a journaled file system, then using the fresh installer install the OS onto the SSD. At the end you will be given an option to transfer your user accounts, apps and data over to the new drive (the wording implied a new system but it will also work between drives on the same system) This is Migration Assistant doing its work! How to transfer data to your new Mac from your old Mac
Lastly, if you did manage to damage your SATA cable follow this guide MacBook Pro 13" Unibody Mid 2010 Hard Drive Cable Replacement